A Characterization of Scoring Rules for Linear Properties

Jacob D. Abernethy, Rafael M. Frongillo
Proceedings of the 25th Annual Conference on Learning Theory, PMLR 23:27.1-27.13, 2012.

Abstract

We consider the design of proper scoring rules, equivalently proper losses, when the goal is to elicit some function, known as a property, of the underlying distribution. We provide a full characterization of the class of proper scoring rules when the property is linear as a function of the input distribution. A key conclusion is that any such scoring rule can be written in the form of a Bregman divergence for some convex function. We also apply our results to the design of prediction market mechanisms, showing a strong equivalence between scoring rules for linear properties and automated prediction market makers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v23-abernethy12, title = {A Characterization of Scoring Rules for Linear Properties}, author = {Abernethy, Jacob D. and Frongillo, Rafael M.}, booktitle = {Proceedings of the 25th Annual Conference on Learning Theory}, pages = {27.1--27.13}, year = {2012}, editor = {Mannor, Shie and Srebro, Nathan and Williamson, Robert C.}, volume = {23}, series = {Proceedings of Machine Learning Research}, address = {Edinburgh, Scotland}, month = {25--27 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v23/abernethy12/abernethy12.pdf}, url = {https://proceedings.mlr.press/v23/abernethy12.html}, abstract = {We consider the design of proper scoring rules, equivalently proper losses, when the goal is to elicit some function, known as a property, of the underlying distribution. We provide a full characterization of the class of proper scoring rules when the property is linear as a function of the input distribution. A key conclusion is that any such scoring rule can be written in the form of a Bregman divergence for some convex function. We also apply our results to the design of prediction market mechanisms, showing a strong equivalence between scoring rules for linear properties and automated prediction market makers.} }
Endnote
%0 Conference Paper %T A Characterization of Scoring Rules for Linear Properties %A Jacob D. Abernethy %A Rafael M. Frongillo %B Proceedings of the 25th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2012 %E Shie Mannor %E Nathan Srebro %E Robert C. Williamson %F pmlr-v23-abernethy12 %I PMLR %P 27.1--27.13 %U https://proceedings.mlr.press/v23/abernethy12.html %V 23 %X We consider the design of proper scoring rules, equivalently proper losses, when the goal is to elicit some function, known as a property, of the underlying distribution. We provide a full characterization of the class of proper scoring rules when the property is linear as a function of the input distribution. A key conclusion is that any such scoring rule can be written in the form of a Bregman divergence for some convex function. We also apply our results to the design of prediction market mechanisms, showing a strong equivalence between scoring rules for linear properties and automated prediction market makers.
RIS
TY - CPAPER TI - A Characterization of Scoring Rules for Linear Properties AU - Jacob D. Abernethy AU - Rafael M. Frongillo BT - Proceedings of the 25th Annual Conference on Learning Theory DA - 2012/06/16 ED - Shie Mannor ED - Nathan Srebro ED - Robert C. Williamson ID - pmlr-v23-abernethy12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 23 SP - 27.1 EP - 27.13 L1 - http://proceedings.mlr.press/v23/abernethy12/abernethy12.pdf UR - https://proceedings.mlr.press/v23/abernethy12.html AB - We consider the design of proper scoring rules, equivalently proper losses, when the goal is to elicit some function, known as a property, of the underlying distribution. We provide a full characterization of the class of proper scoring rules when the property is linear as a function of the input distribution. A key conclusion is that any such scoring rule can be written in the form of a Bregman divergence for some convex function. We also apply our results to the design of prediction market mechanisms, showing a strong equivalence between scoring rules for linear properties and automated prediction market makers. ER -
APA
Abernethy, J.D. & Frongillo, R.M.. (2012). A Characterization of Scoring Rules for Linear Properties. Proceedings of the 25th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 23:27.1-27.13 Available from https://proceedings.mlr.press/v23/abernethy12.html.

Related Material